Problems 85 2.8-1. Given in Fig. P2.8-1 are two digital-filter structures, or realizations, for second-order filters. (a) Write the difference equation for the 3D structure of Fig. P2.8-1(a), expressing y(k) as a function of y(k-1) and e(k-1). (b) Derive the filter transfer function Y2V/E(2) for the 3D structure by taking the 2-transform of the equa- tion in part (a). (c) Write the difference equation for the ID structure of Fig. P2.8-1(b). Two equations are required, with one for fk) and one for y(k). (d) Derive the filter transfer function Y(2)/E(2) for the ID structure by taking the z-transform of the equa- tions in part (c) and eliminating F(z). (Y) (k) B₂ B₁ Bo y(k) T (a) by b₁ y(k) (k) y(k) T T bo d FIGURE P2.8-1 Digital-filter structures: (a) 3D; (b) 1D. (b) do